Spin Measurements of Accreting Black Holes

Remarkably, an astrophysical black hole has only two attributes: its mass and its spin angular momentum. Spin is often associated with the exotic behavior that black holes manifest such as the production of relativistic and energetic jets. In this thesis, we advance one of the two primary methods of measuring black hole spin, namely, the continuum-fitting method by (1) improving the methodology; (2) testing two foundational assumptions; and (3) measuring the spins of two stellar-mass black holes in X-ray binary systems. Methodology: We present an empirical model of Comptonization that self-consistently generates a hard power-law component by upscattering thermal accretion disk photons as they traverse a hot corona. We show that this model enables reliable measurements